As a conventional substrate with fine projections and depressions, a substrate with fine projections and depressions which is obtained by coating a glass substrate with a solution containing tetraethoxysilane and polyethylene glycol by a sol-gel process and pressing a die against the coated glass substrate to transfer a pattern of projections and depressions to the coating film is reported in Japanese Patent Laid-Open Publication No. 62-225273. Further, a substrate with fine projections and depressions which is obtained by coating a glass substrate with a solution containing an organoalkoxysilane such as methyltriethoxysilane and pressing a die against the coated glass substrate to transfer a pattern of projections and depressions to the coating film is reported in Japanese Patent Laid-Open Publication No. 6-114334. Still further, a substrate with fine projections and depressions which is obtained by pressing a die against a composite comprising compounds obtained by hydrolyzing and polycondensing dimethylalkoxysilane and phenyltrialkoxysilane to transfer a pattern of projections and depressions to the composite is reported in Japanese Patent Laid-Open Publication No. 11-314927.
However, although the substrate with fine projections and depressions which is prepared by using the solution containing tetraethoxysilane and polyethylene glycol has the characteristic that the film becomes completely inorganic and amorphous when the substrate is calcined at about 350° C., the substrate also has the problems that the inverse of the pattern of the die cannot be transferred completely due to the shrinkage of the film by the calcination and that cracks are produced by the shrinkage stress of the film when the thickness of the film is 1 μm or larger. Meanwhile, the substrate with fine projections and depressions which is prepared by using the solution containing an organoalkoxysilane such as methyltriethoxysilane has such an excellent characteristic that the inverse of the pattern of the die can be transferred completely and the film can be thickened since the film has low shrinkage, it is difficult to control the refractive index of the film actively. In addition, although the substrate with a pattern of fine projections and depressions which is transferred to the substrate by pressing the die against the composite comprising the compounds obtained by hydrolyzing and polycondensing dimethylalkoxysilane and phenyltrialkoxysilane has excellent heat resistance and a thick-film pattern can be formed easily, it also has such a problem that the film has low film hardness.